TUYMAADA 2007 Problem 2

Two polynomials $f(x)=a_{100}x^{100}+a_{99}x^{99}+\dots+a_{1}x+a_{0}$ and $g(x)=b_{100}x^{100}+b_{99}x^{99}+\dots+b_{1}x+b_{0}$ of degree $100$ differ from each other by a permutation of coefficients. It is known that $a_{i}\ne b_{i}$ for $i=0, 1, 2, \dots, 100$ . Is it possible that $f(x)\geq g(x)$ for all real $x$ ?